Fix prefactor of dynamical phase in summary. Fixes #6.

src/adiabatic_proof.md

@@ -209,10 +209,10 @@ This means that:
 * It acquires two phases shifts depending on the evolution. The dynamical phase, $\theta_n(t)$, and the geometrical phase $\gamma_n(t)$. They are given as,
 
 $$
-\theta_n(t) = i \int_0^t E_n(t') \rangle dt', \quad \gamma_n(t) = i \int_0^t \langle{\psi_n| \dot\psi_n} \rangle dt'.
+\theta_n(t) = -\frac{1}{\hbar} \int_0^t E_n(t') \rangle dt', \quad \gamma_n(t) = i \int_0^t \langle{\psi_n| \dot\psi_n} \rangle dt'.
 $$
 In order for this description to hold, we require that the system evolves slowly enough. That is, the following condition must be satisfied at all times:
 $$
 \frac{\hbar \overline{\langle \psi_n | \dot H |\psi_m\rangle} }{\overline{E_n - E_m}^2} << 1, \quad n \neq m.
 $$
-Here, the overline indicates the largest matrix element, and the smallest energy difference.
+Here, the overline indicates the largest matrix element, and the smallest energy difference.
\ No newline at end of file